Respuesta :
Answer:
128 cm²
Step-by-step explanation:
Given the scale factor of 2 similar figures is a : b , then
ratio of areas = a² : b²
Here the scale factor = 3 : 4 , thus
ratio of areas = 3² : 4² = 9 : 16
let x be the area of the larger figure then by proportion
[tex]\frac{9}{72}[/tex] = [tex]\frac{16}{x}[/tex] ( cross- multiply )
9x = 1152 ( divide both sides by 9 (
x = 128
Thus area of larger figure is 128 cm²
The required area of the bigger shape is 128 cm².
The linear scale factor of two similar shapes is in ratio 3:4. the area of the smaller shape is 72cm square. To determine the area of the bigger shape.
What is the Ratio?
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Linear scale factor ratio of two similar shapes = 3:4
Let the area of the bigger shape = x²
Area of the smaller shape = 72
Now since the ratio is linear = 3 : 4
squaring the ratio = 3²:4²
= 9:16
Now the ratio of the are = 72: x²
Equating the ratios
72/x² = 9/16
x² = 16/9 * 72
x² = 1.77 * 72
x² = 128
Thus, the required area of the bigger shape is 128 cm².
Learn more about Ratio here:
brainly.com/question/13419413
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